顶端受集中力偶或表面受均匀载荷的圆柱型正交各向异性楔:佯谬的解决  

A Method of Resolving the Paradoxes Occurred in the Cylindrical Couple or Uniform Tractions

作　　者：丁皓江[1] 彭南陵[1] 李文先 

机构地区：[1]浙江大学,南昌大学

出　　处：《应用力学学报》1997年第4期37-45,共9页Chinese Journal of Applied Mechanics

基　　金：南昌大学青年基金

摘　　要：对楔顶角为２α的圆柱型正交各向异性楔，其顶端受集中力偶的经典解当α满足ｔｇλα＝λα（λ＝（ａ６６＋２ａ１２＋２ａ１１）／ａ１１，ａ６６、ａ１２、ａ１１为弹性常数）时，应力成为无穷大；其表面受均匀载荷的经典解当α满足ｓｉｎλα＝０（对称变形）或ｔｇλα＝λα（反对称变形）时，也有同样问题。For a cylindrical orthogonal anisotropic wedge of angle 2α, the classical solution for the wedge subject to a concentrated couple at the vertex becomes infinite when α satisfies tgλα=λα(λ=(a66+2a12+2a11)/a11,　a66,　where　a12,　a11　are elastic constants), this is also true for the classical solution for the wedge subject to uniform tractions on the surfaces when α satisfies sin　λα=0　(symmetric deformations) or tgλα=λα　(antisymmetric deformations). The two paradoxes are resolved through the superposition of the homogeneous solutions in the paper.

关 键 词：楔体 佯谬 应力奇异性 正交各向异性 弹性力学 

分 类 号：O343.8[理学—固体力学]